The velocity-time graph for a cycle is shown.
104
8
8
Velocity (m/s)
2
0
0 2 4 6 8 10 12 14 16 18 20
Time (seconds)
a) Work out the distance travelled on the cycle in the first 14 seconds.
b) Work out the acceleration in the first 4 seconds.

Answer:

perimeter are the adding up of all side in a figure. Area is length times width and volume is length x width x height

Step-by-step explanation:

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Answer:

Volume: The amount a container can hold.

Area: The space a flat shape covers.

Perimeter: The length around an object.

Step-by-step explanation:

There's a slight problem with your question, but we'll get to that...

Consecutive terms of the sequence are separated by a fixed difference of 21 (22 = 1 + 21, 43 = 22 + 21, 64 = 43 + 21, and so on), so the n-th term of the sequence, a (n), is given recursively by

• a (1) = 1

• a (n) = a (n - 1) + 21 … … … for n > 1

We can find the explicit rule for the sequence by iterative substitution:

a (2) = a (1) + 21

a (3) = a (2) + 21 = (a (1) + 21) + 21 = a (1) + 2×21

a (4) = a (3) + 21 = (a (1) + 2×21) + 21 = a (1) + 3×21

and so on, with the general pattern

a (n) = a (1) + 21 (n - 1) = 21n - 20

Now, we're told that the sum of some number N of terms in this sequence is 2332. In other words, the N-th partial sum of the sequence is

a (1) + a (2) + a (3) + … + a (N - 1) + a (N) = 2332

or more compactly,

\(\displaystyle\sum_{n=1}^N a(n) = 2332\)

It's important to note that N must be some positive integer.

Replace a (n) by the explicit rule:

\(\displaystyle\sum_{n=1}^N (21n-20) = 2332\)

Expand the sum on the left as

\(\displaystyle 21 \sum_{n=1}^N n-20\sum_{n=1}^N1 = 2332\)

and recall the formulas,

\(\displaystyle\sum_{k=1}^n1=\underbrace{1+1+\cdots+1}_{n\text{ times}}=n\)

\(\displaystyle\sum_{k=1}^nk=1+2+3+\cdots+n=\frac{n(n+1)}2\)

So the sum of the first N terms of a (n) is such that

21 × N (N + 1)/2 - 20N = 2332

Solve for N :

21 (N ² + N) - 40N = 4664

21 N ² - 19 N - 4664 = 0

Now for the problem I mentioned at the start: this polynomial has no rational roots, and instead

N = (19 ± √392,137)/42 ≈ -14.45 or 15.36

so there is no positive integer N for which the first N terms of the sum add up to 2332.

Solution:

Note that:

This means...

Refer to table uploaded~

The expression for the height of the hot air balloon m minutes after it begins its descent is 576-25m and to reach a height of 100 feet the balloon will take 19.04 minutes.

Given that the height of ballon is 576 feet and its height is decreasing at a rate of 25 feet per minute.

We are required to find the expression for the height of the hot air balloon m minutes after it begins its descent and the height after which the balloon will be at a height of 100 feet.

Expression is combination of numbers, symbols, fraction,etc.

Let the number of minutes be m.

The expression which will show the height of balloon is 576-25m.

Height required will be 100.

100=576-25m

25m=476

m=476/25

m=19.04 minutes

Hence the expression for the height of the hot air balloon m minutes after it begins its descent is 576-25m and to reach a height of 100 feet the balloon will take 19.04 minutes.

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Answer:

True

Step-by-step explanation:

We actually can use Sine, Cos, or Tangent to solve for the angles, which would give the angle, but graphing it came up with an Obtuse Scalene triangle.

The area of the whole mosaic is 455.11 square feet

From the question, we have the following parameters that can be used in our computation:

The area of the whole mosaic is calculated as

Area = Area of the array * the square of each length

using the above as a guide, we have the following:

Area = 8 * 8 * (2 2/3)²

Evaluate

Area = 455.11

Hence, the area of the whole mosaic is 455.11 square feet

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The sum of all the angles that are labeled in the given vertex is 294°

In a single vertex, the three angles around the vertex are given as 55°, 64°, and 175°

We have to find the sum of all the angles that are labeled in the given single vertex.

A vertex is a point two or more lines meets.

It is the corner of a geometrical shape.

Example:

A square has 4 corners so it has 4 vertexes.

A cube has 8 corners so it has 8 vertexes.

We will add all the different angles in the single vertex as shown in the figure below.

Let,

Angle A = 55°

Angle B = 64°

Angle C = 175°

The sum of all the angles that are labeled is:

= Angle A + Angle B + Angle C

= 55° + 64° + 175°

= 294°

The sum of all the angles that are labeled in the given vertex is 294°

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9!

---------------

2! x 2! x 2!

There were 13 small boxes shipped and 6 large boxes shipped.

Let's denote the number of small boxes as 's' and the number of large boxes as 'l'.

According to the given information, the volume of each small box is 6 cubic feet, so the total volume of all small boxes can be calculated as 6s cubic feet.

Similarly, the volume of each large box is 13 cubic feet, so the total volume of all large boxes can be calculated as 13l cubic feet.

We are also given that the combined volume of all the boxes is 156 cubic feet, so we can write the equation:

6s + 13l = 156 ...(1)

Additionally, we know that a total of 19 boxes were shipped, so we can write another equation:

s + l = 19 ...(2)

Now, we have a system of equations (equation 1 and equation 2) that we can solve simultaneously to find the values of 's' and 'l'.

To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method here.

From equation 2, we can rewrite it as s = 19 - l.

Substituting this value of s into equation 1, we get:

6(19 - l) + 13l = 156

Simplifying the equation:

114 - 6l + 13l = 156

Combining like terms:

7l = 42

Dividing both sides by 7:

l = 6

Now, we can substitute this value of l back into equation 2 to find the value of s:

s + 6 = 19

s = 13

The number of small boxes shipped is 13, and the number of large boxes shipped is 6.

There were 13 small boxes shipped and 6 large boxes shipped.

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Answer:

-11

Step-by-step explanation:

Answer:

\(x=-11\)

Step-by-step explanation:

\(-1=\frac{\left(5+x\right)}{6}\)

Switch sides:

\(\frac{\left(5+x\right)}{6}=-1\)

Multiply both sides by 6:

\(\frac{6\left(5+x\right)}{6}=6\left(-1\right)\)

\(5+x=-6\)

Subtract 5 from both sides:

\(5+x-5=-6-5\)

\(x=-11\)

Answer:

1.) y > - 1/5

2.) y < -2

Step-by-step explanation:

-5y < 1

y > - 1/5

6y < -12

y < - 12/6

y < -2

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Answer:

( − ∞ , − 12 )

Step-by-step explanation:

The result can be shown in multiple forms.

Inequality Form:

−  5  <  1  and  6 y  <  − 12

Interval Notation:

( − ∞ , − 12 )

The significant figures are the digits of the number that provide information about the measurement that number represents.

In this case, all the digits has to be included because all of them are giving information about the measurement.

Answer:

is c

Step-by-step explanation:

i took the test

Answer:

Its C,  No, some of the terms changed signs.

Step-by-step explanation:

I did it on edge 2020

Answer:

A byte is 8 bits.

If a position function, s(t) = 2t⁴ - 9t³ - 6t² - 8, where t and s be time and distance, then the acceleration of the car at t=2 seconds is equals to the -24 m/s².

Generally acceleration means the speed is changing. Acceleration is defined as the rate of change of velocity of a particle with respect to time, in terms of both speed and direction. Mathematical formula is written as, a = dv/dt

where, dv --> change in velocity

dt --> change in time

a --> acceleration

so, acceleration is also vector quantity and units is m/sec² or cm/s² etc. We have a position function of car traveling along a highway and defined as, s(t) = 2t⁴ - 9t³ - 6t² - 8

where t --> measured in seconds and

s --> measured in meters.

Velocity of car is equals to rate of change of position of car with respect to the time,t that is \(v(t)=\frac{d( s(t))}{dt}\).

So, first take the derivative to find the expression for the velocity of the particle.

=> v(t) = s'(t) = 8t³ - 27t² - 12t (using derivative rule)

Now, differentiate v(t) function w.r.t t for acceleration of car

=> \(a(t) = \frac{d(v(t))}{dt}\)

\(=\frac{d(8 {t}^{3} - 27{t}^{2} - 12t)}{dt}\)

= 24t² - 54t - 12

Acceleration of car when t = 2 seconds,

= 24(2)² - 54×2 -12

= 96 - 108 -12 = -24

Hence, required value is -24 m/s².

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Answer:

\((a - b)(a + b) \\ a(a + b) - b(a + b) \\ {a}^{2} + ab - ab - {b}^{2} ( + ab \: and \: - ab \: cancel) \\ {a}^{2} - b ^{2} \)

I hope it helped U

stay safe stay happy

Answer:

The answer is B. i.e. 6.6units.

Answer:

39

Step-by-step explanation:

put them in order least to greatest, then subtract 108-69=39

The number of color sequences possible when removing five balls one at a time depends on the number of different colors the balls have.

If there are C different colors, the number of color sequences possible is C^5 (C raised to the power of 5), since for each ball you remove, you have C options for its color.

The number of combinations of colors possible when removing five balls one at a time is given by the binomial coefficient "C choose 5", which represents the number of ways to choose 5 balls out of C different balls, ignoring the order in which they are chosen.

The binomial coefficient can be calculated as:

C choose 5 = C! / (5! * (C-5)!).

Here, "!" denotes the factorial symbol, which is the product of all positive integers up to that number (e.g. 5! = 5 * 4 * 3 * 2 * 1 = 120).

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Answer: 1/2x^3

Explanation: The volume of a space figure is basically the area multiplied to it’s height. In this case, the triangle’s area formula is 1/2x^2, and since the height is also represented by x, multiplying the two values will give you 1/2x^3.

The solution is, V =1/2*x³ cubic units., is the expression represents the volume of the prism, in cubic units.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

Given the information

A right triangular prism has the height is equal to the leg length of the base.

The right triangles have 2 sides with a length of x

=> the height  = x  

As we know, the formula used to determine the volume of a right triangular prism is:

V = The base area * the height

In this situation, we have

V = 1/2 * ( x * x ) * x

<=> V = 1/2*x³ cubic units  

Hence, The solution is, V =1/2*x³ cubic units., is the expression represents the volume of the prism, in cubic units.

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0.60792 liters x 1000 = 607.92 mL

Multiplying the volume in liters by 1000 converts it to milliliters.

The equation of the parent square root function to represent the equation of the graphed function will be, y=√x-2

According to the statement

we have to show the square root function as a equation in the graphical representation.

So,

we know that the definition of a

Graph a diagram showing the relation between variable quantities, typically of two variables and it also show the relation between more than two variables.

Now, we know that the definition of Equation is a mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

And the equation obtained from the graph is a y=√x-2 by a some calculations in the graph.

So, The equation of the parent square root function to represent the equation of the graphed function will be, y=√x-2

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The number of each type of coins are as follows:

q = 15 quarters.

d = 30 dimes.

n = 25 nickels.

In order to solve this word problem, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:

Let d represent the number of dimes.

Let q represent number of quarters.

Let n represent number of nickels.

Let T represent total number of coins.

Note: 1 quarter is equal to 0.25 dollar, 1 nickel is equal to 0.5 dollar, and 1 dime is equal to 0.1 dollar.

Translating the word problem into an algebraic equation, we have;

Dimes; d = 2q     .....equation 1.

Nickels; (70 - (q + 2q)) = (70 - 3q)     .....equation 2.

Total coins; T = n + d + q

0.5(70 - 3q) + 2q(0.1) + q(0.25) = 8.00

Multiplying all through by 100, we have:

5(70 - 3q) + 2q(10) + q(25) = 800

350 - 15q + 20q + 25q = 800

350 + 30q = 800

30q = 800 - 350

30q = 450

q = 450/30

q = 15 quarters.

For the number of dimes, we have:

Dimes, d = 2q

Dimes, d = 2(15)

Dimes, d = 30 dimes.

For the number of nickels, we have:

Nickels, n = (70 - 3q)

Nickels, n = (70 - 3(15))

Nickels, n = (70 - 45)

Nickels, n = 25 nickels.

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The mean and range of the same population can differ if there is a significant difference between the sampled respondents.

Between Jayden and Carter, Carter's calculation will provide a better understanding of the population.

The reason is that he sampled more people with a wider time range.

The mean is the average number of minutes it took for the respondents to dress up. The goal of any survey work is to capture a significant size of the population whose opinions can give a true picture of the situation being examined.

In the case of Carter, we see that he took a more sizable amount of the population having randomly selected 7 samples of 10 students. A greater number of respondents will give a truer picture of the factor being surveyed.

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Answer:

false

Step-by-step explanation:

Answer: 24.0825%

Step-by-step explanation:

8.25% as fraction: 33/400

24+33/400

Convert element into fraction: 24x400/400

24x400/400+33/400= 9633/400

Final step: Make it into a decimal

24.0825% is your answer

Answer:

what does 30 yldpri the linear relationship have do with it

Step-by-step explanation:

Answer:

x=21 degrees

Step-by-step explanation:

x degrees and 159 degrees are supplementary angles

this means that x+159=180 degrees

x=21 degrees

Answer:

Step-by-step explanation:

I hope it helps